Cpk •
Cp
- see Natural Tolerance decreases with spec width
- see Natural Tolerance Tolerance • •
decreases with spec width Cp = 1 for centered process - natural tolerance =spec width
Cause and Effect Diagram - Fishbone Diagrams - Ishikawa Diagrams • • • • • • • •
used to identify and organize potential root causes problem solving analysis done by brainstorming common categories - Measurement, Materials, People, Process, Equipment, Environment ask “Why?” 3 times to get to root cause have detailed problem statement at head of fish fish - “effect” need corresponding process map should fit on one 8-½ x 11 page should have all 6 fishbones and at least 3 levels deep
C-bar •
C-bar is the average of all the subgroup C-values in C-Chart
C – Chart • • • •
- see Attribute Attribute Data Control Charts
Count chart a specialized version of U chart used to monitor the number of errors found - occurrences per unit - error count number numbe r of units or subgroup size MUST remain constant consta nt
Census •
count or measurement of the entire en tire population
Continuous Data • •
measured – weigh, timed, can be measured and broken down into smaller parts and still have meaning. Money, temperature and time are continous.Volume continous.Volume (like volume of water or air) and size are continuous data.
Control Charts •
indicate stability over time
Chart Rules – Control Charts • •
P-chart or NP-chart - count number of items in error or defectives U-chart or C-chart - count number of errors or defects in items
Common causes control limits
-
see variation
• •
Provide boundaries for a process running in control based upon process data
CTQ - Critical to Quality •
•
• •
key measurable characteristics of a product or process whose performance standards or specification limits must be met in order to satisfy the customer CTQ’s CTQ’s represent the product or service characteristics cha racteristics that are defined by the customer (internal or external). They may include the upper and lower specification limits or any other factors related to the product or service. the product or service characteristics that are defined by the customer as critical to their needs what the customer expects of a product
DATA Attribute Data Control Charts • • • • • •
Attribute data - qualitative data that can be counted for recording and analysis good/bad, yes/no the average and dispersion are closely related; therefore, only one chart needed P-Chart – proportions percent defective with variable or c onstant sample size NP-chart– number of defectives with constant sample size C-Chart – count of defects with constant con stant sample size U-Chart – defects per unit with variable or constant sample size
Variable Data Control Charts • • • •
Variable data – measured - two types (Discrete) count data and (Continuous) data X and MR – for financial, mtce costs, efficiency ratings, productivity – (usually 2 charts) X-bar and Range X-bar and S (standard deviation) – X-bar for sa mple average and “S” to monitor process dispersion
•
Defect •
non-conformities – a single characteristic not meeting defined requirements
Defective •
non-conformance – contains one or more defects
DET - see FMEA Discrete Data •
counted (usually in whole numbers)
DMAIC • • •
•
Define – project charter, problem statement, scope, goals, resources, financial, process maps Measure – collect data, process maps, fishbone, Pareto, QFD, need accuracy & precision Analyze - root cause is verified, hypothesis testing (verifying assumptions and predictions regarding the relationship between process inputs and the CTQ values) Improve – brainstorming for ideas & solutions to problems identified in Analyze phase
• • •
Control – helps to reduce variation va riation in the process and eliminate defects Control - project responsibilities transition from process improvement team to operations team Six Sigma Methodology used for process improvement
DPMO • •
(defects per million opportunities)
defect level for a process number of defects divided by number of opportunities multiplied by one million
DOE - Design of Experiments • • •
•
math & statistics used in the design & analysis analysis phase of an experiment to find best settings optimize a process, reduce common cause variation, and maximize ROI organized method for determining the relationship between factors (Xs) affecting a process and the output of that process (Y) experimental methods used to quantify indeterminate measurements of factors and interactions between factors statistically through observance of forced changes made methodically as directed by mathematically systematic tables
Fish Bone
- see Cause and Effect Diagram
FMEA - Failure Mode and Effects Analysis • • • • • •
tool to identify where in the process if the source of failure RPN - Risk Priority Number relative risk of a particular failure mode = SEV x OCC x DET OCC or Likelihood of Occurrence rating - likelihood of the failure occurring DET – detection rating measures likelihood current control system will detect cause or failure SEV – severity rating how significant the impact of the effect is to the customer vital x’s (root causes from low-level fishbones) go into potential cause column and can o ccur in more than one process step
Gauge R&R •
Repeatability & Reproducibility
Gauge Repeatability •
how consistently same operator or measurement system measures same even over time
Gauge Reproducibility •
how consistently several operators or measurement systems measure same even over time
Histogram •
tool used in the Measure phase to illustrate shape, central tendency, and dispersion of data
Leverage • • •
applying proven methods to other projects via lessons learned - share ideas & best practices reduces costs, increase efficiency, improve customer service identifying “spin-off” projects that can benefit
Master Attribute
standard or correct answer in an Attribute Gauge R & R study
•
MR = Moving Range Mean • • • •
arithmetic average the statistic most often used as the measure of cen tral tendency or center of data represented by Greek symbol “μ” (pronounced mu) center line (process average) in a control chart between UCL and LCL
Measurement systems • • • • •
see Gauge Reproducibility and Gauge Reproducibility Accuracy – how close the average are equal to the target Precision – variation in repeated measurement of the same event Linearity – performance over a range of events Stability – performance over time
Measurement system analysis •
used to validate the measurement system s ystem
natural tolerance •
•
Natural tolerance is also called “6 sigma” becau se it is defined as 6 times the population pop ulation standard deviation of the individual observations. 3 sigma on each side of the process mean Cp CpU CpL Cpk Cpk
= = = =
Proces Processs capabil capability ity potent potential ial = spec spec width/ width/nat natura urall tolera tolerance nce = (U - L) / 6 sigm sigmaa Upper per capa apability index = (U - Mean) / 3 sigma gma Lower capabi pabillity index = (Mean - L) / 3 sigma Proc Proces esss capab capabil ilit ity y inde index x = Mini Minimu mum m of CpU CpU and CpL CpL
If the process capability potential, Cp, is greater than 1.0 , the specification limits are wider than the natural tolerance, and the process has the potential for meeting specifications if held in control at a mean of (U - L)/2.
net profit •
selling price minus costs
NP-Bar •
centerline or process average of all subgroups in NP-Chart
NP - Chart • • • • •
- see Attribute Attribute Data Control Charts
a specialized version of the P-chart used when your sample size is constant used to monitor the number rather than the proportion of items with a defined characteristic subgroups MUST be equal size used to track the actual number n umber of defective items or the actual number of good items average and dispersion are closely related; therefore, only one chart is required
OCC - see FMEA
Pareto Chart • • • • • • • • • •
simple bar chart where the height of each bar represents the frequency of a given category can be used to rank problems by their dollar costs rather than frequency prioritize problems from those that happen most often to those that happen least often cumulative percentage curve added to show ∑% of occurrences up to and including a given category stratification - systematic subdivision of a problem into its subcomponents identifies which opportunity or problem the team should focus on categories are listed in order of frequency – higher on left height of each bar represents the frequency of a given category 80-20 rule - 80% of occurrences of problems are accounted for by 20% of the categories of problems developed by Italian economist named Vilfredo Pareto
P-Chart • • •
• • •
- see Attribute Data Control Control Charts Charts
monitor proportion or percentage values plotted will always be a proportion and result in a number from zero to one P-chart is required to monitor the process average and dispersion. With With attribute data, the average and dispersion are closely related. Therefore, only one chart is needed. sub-group sample sizes may vary. vary. The control limits will vary but the centerline stays constant. larger sub-group size has narrower limits because larger sample size reduces sampling error With unequal subgroup sizes, p-bar is a weighted average of the individual sub-group proportions. A weighted average just means the individual p’s don’t all carry the same weight in the calculation of p bar.
Problem statement •
data-driven statement that does not include opinions o pinions on root causes or possible solutions
Process capability • • • • •
the extent to which a stable process is able to meet specifications assessed using either continuous data or discrete data when using attribute data should be expressed as percent, PPM, PPB defective, DPMO, etc. assessed with a histogram with specification limits capable process has a high Cp value and Cpk=Cp
Process Capability Index: distance of mean to near spec Cpk = ―――――――――――― half the natural tolerance)
Process Capability Index (if centered): voice of customer (spec width) Cp = ―――――――――――――― voice of process (natural tolerance or 6 sigma)
Process out-of-control - see process shift
process shift • • •
a cluster of eight consecutive data points either all above or below the median a point outside of control limits is indication that process may be shifting process shift makes it inappropriate to calculate the ov erall average (or standard deviation) of the data
Process maps • • • • • • • • • •
shows the inter-relationships of the steps in a process used to discipline teams to produce solutions that a re definable, repeatable, predictable and measurable walk the process clearly define the boundaries of the process should include data, sigma level, COPQ, defect rate, flow rate “as is" include rework loops oval – starting or stopping point rectangle – process step or action diamond - decision
projects selecting potential projects consider - resource availability, availability, reward, complexity, complexity, risk
Project Charter • • • • •
set expectations and obtain buy-in on scope, goal, and resources accelerate the acquisition of resources avoid scope creep documentation easy and effective means to document a Six Sigma project
Project selection •
considerations = Complexity, Risk, Reward, Resource availability
Quality Function Deployment - QFD •
tool used to analyze customer requirements
R = Range
Root Causes • • •
often found in low-level fishbones during analyze phase easier to find the root cause of a problem that is detected as it is happening h appening see Cause and Effect Diagram
ROI = Return On Investment • • • • • • • •
for Six Sigma project is calculated by dividing the project savings by the project cost used to measure the impact of a Six Sigma project on business results Reduced operating costs Increase in operating efficiencies Improved morale Communicating project savings Sharing ideas and best practices Identifying “spin-off” projects
RPN – see FMEA S = Standard Deviation S-Chart •
- see standard deviation
- see Variable Data Control Control Charts Charts
to monitor process dispersion
Sample • • •
subset of the population every element in a sample is also an element of the population Stratified sampling – grouping members into similar subgroups before sampling
Sample Mean • •
used to estimate the population mean sample = subset of the population
Savings • •
soft = non-tangible – time, customer satisfaction, morale hard = money, cost, can be counted, direct impact upon the company's bottom line
Scatter Diagram • •
•
shows the type of correlation between two va riables strength of the relationship between two variables is determined visually by the tightness of the cluster of points on the scatter diagram around the line of best fit drawn through the points extrapolation is used to predict a value outside the range of the data plotted
Scope Creep • •
Tendency for project to expand scope limited by clearly defining boundaries
SEV - see FMEA Sigma -
see standard deviation
SIPOC • •
Suppliers, Inputs, Process, Outputs and Customers the system view of a process
Six Sigma • • • • • •
∂
a commitment to your customers. a method that uses best management manage ment ideas and practices for flexible system for process improvement a means to stretch your thinking with respect to quality and customer satisfaction customer focused fact-based strategy focused on process improvement, variation reduction and defect elimination uses two types types of data - continuous and discrete discrete
solution design matrix •
used to organize alternative solutions
Spec width = USL – LSL Special causes
-
see variation
Specification Limits •
used to determine if a product meets customer requirements
Standard Deviation • • • • • • •
=
sigma
measures dispersion from the mean – shows on a verage how far the values are from the mean “s” represents standard deviation of a sample sigma or Standard Deviation is used in combination with X Bar to describe the "Normal Distribution To find six sigma, calculate sigma, multiply by 6, and add or subtract the result to the calculated mean. 68.27% of normal population lies within +/- one sigma from its average (mean) μ 95.45% of normal population lies within +/- two sigma’s from its average (mean) μ 99.73% of normal population lies within +/- three sigma ’s from its average (mean) μ Sigma, (Standard Deviation), Formula
= n or (n - 1)
Statistics • • • •
Uses Qualitative and Quantitative data types Systematic Sampling - uses a rule or pattern to select elements from the population to form the sample Qualitative = discrete data – counted , Not measured Quantitative data - continuous data - different different depending on types of questions questions
X-bar Chart •
- see Variable Variable Data Control Charts
used to monitor central tendency
X-bar and S Chart
- see Variable Data Control Control Charts Charts
__
X-bar = X • •
•
mean or average of sample typically charted on a line control chart with the center line being X Double Bar, (an average of the averages), and upper control limits and lower control limits We use averages because they the y are more susceptible to change than single values.
XmR Charts • •
- see Variable Variable Data Control Charts
control chart which uses a moving range. Typically Typically two but can have a larger range usually used when one measurement is available ava ilable for each subgroup
Upper Control Limit •
control limit for points above the central line in a control chart
U - Chart • • • • • • •
UCL
- see Attribute Attribute Data Control Control Charts Charts
a graph of the number of errors per unit - - error rate unit may be time, area, machines, or length value of U could be a number greater than 1 equal sample or subgroup size is NOT a requirement used to track the number of occurrences of some event per unit average and dispersion are closely related. Therefore, only ONE char t is needed larger subgroup size = narrower limits (larger sample size size reduces sampling error)
Variable •
a characteristic or property of an individual element in a population or sample
Variation • • •
Common Cause - causes of variation that are inherent in a process over time. They affect every outcome Common cause – variation inside control limits limits - do NOT adjust process Special Cause - relatively large, unusual variation usually comes from outside the process
Z value •
•
Z value is a data point's position between the mean and another location (usually mean) as measured by the number of standard deviations. Z is a measure of process capability capab ility and corresponds to the process sigma value that is reported by the businesses. For example, a 3 sigma process means tha t three standard deviations lie between the mean and the nearest specification limit. Three is the Z value.
Costs
Costs
Costs
appraisal costs • • • • • • • •
inspection costs incurred to identify defective products before the p roducts are shipped to customers Test and inspection of incoming materials Test and inspection of in-process goods Final product testing and inspection Supplies used in testing and inspection Supervision of testing and inspection activities Depreciation & maintenance of test equipment field testing and appraisal at customer site
COPQ • • • •
(Cost Of Poor Quality)
rework loop cost = (Defect rate) x (Volume) (Volume) x (Cost of rework per unit) penalty from not performing work correctly the first time or not meeting customer ’s expectation cost categories = appraisal, internal failure, prevention, external most often calculated in the design stage of the Six Sigma Methodology
Entitlement cost •
cost of doing the right thing right the first time
Internal failure Costs • •
Internal failure costs result from identification of defects before shipping to customers Costs include scrap, rejected products, reworking of defective units, and downtime
External Failure Costs • •
defective product is delivered to customer costs include warranty, repairs and replacements, product recalls, liability arising from legal actions against a company, and lost sales arising from a reputation for poor quality
Prevention Costs • •
Prevention costs support activities whose purpose is to reduce the number of defects. Examples - statistical process control, quality engineering, training, and tools tools
Sigma to DPMO to Yield to Cpk Table
Sigma
DPMO
Yield
Cpk
1.5
500,000
50 %
0.50
3.00
66,800
93.320%
1.00
3.50
22,700
97.730%
1.17
4.00
6,210
99.3790%
1.33
4.50
1,350
99.8650%
1.50
5.00
23 0
99.9770%
1.67
6.00
3.4
99.99966%
2.00
Assumptions No analysis would be complete without properly noting the assumptions made. In the above table, tab le, we have assumed that the standard sigma shift of 1.5 is appropriate, the data is normally distributed, and the process is stable.
